SpringerLink
Log in

Global Asymptotic Stability for Discrete-Time SEI Reaction-Diffusion Model

  • Conference paper
  • First Online:
Mathematics and Computation (IACMC 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 418))

Included in the following conference series:

Abstract

The global stability of solutions for a discrete-time globally dispersed reaction-diffusion SEI epidemic model with individual immigration is investigated in this work. The global stability is addressed using the Lyapunov functional after giving a discrete form of the reaction-diffusion SEI epidemic model. As in the continuous case, the unique steady-state is proven to be globally stable in the presence of diffusion. To validate the findings of this study, some numerical simulations are provided.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Abdelmalek, S., Bendoukha, S.: Global asymptotic stability for a SEI reaction-diffusion model of infectious diseases with immigration. Int. J. Biomath. 11, 1850044 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  2. Abdelmalek, S., Bendoukha, S.: Global asymptotic stability of a diffusive SVIR epidemic model with immigration of individuals. Electron. J. Differ. Equ. 129(324), 1–14 (2016)

    MathSciNet  MATH  Google Scholar 

  3. Sigdel, R.P., McCluskey, C.C.: Global stability for an SEI model of infectious disease with immigration. Appl. Math. Comput. 243, 684–689 (2014)

    MathSciNet  MATH  Google Scholar 

  4. Xu, L., Han, R.: Global stability for a discrete space-time Lotka-Volterra system with feedback control. Complexity 2020, 2960503 (2020)

    MATH  Google Scholar 

  5. Hioual, A., Ouannas, A.: On fractional variable-order neural networks with time-varying external inputs. Innovat. J. Math. 1, 52–65 (2022)

    Article  Google Scholar 

  6. Wang, B., Ouannas, A., **a, W.F., Jahanshahi, H., Alotaibi, N.D.: A hybrid approach for synchronizing between two reaction-diffusion systems of integer- and fractional-order applied on certain chemical models. Fractals, preprint (2022)

    Google Scholar 

  7. Gasri, A., Ouannas, A., Khennaoui, A.A., Grassi, G.: Chaotic fractional discrete neural networks based on the Caputo h-difference operator: stabilization and linear control laws for synchronization. Eur. Phys. J. Spec. Top. 2022, 1–15 (2022)

    Google Scholar 

  8. Shatnawi, M.T., Djenina, N., Ouannas, A., Batiha, I.M., Grassie, G.: Novel convenient conditions for the stability of nonlinear incommensurate fractional-order difference systems. Alex. Eng. J. 61, 1655–1663 (2022)

    Article  Google Scholar 

  9. Hioual, A., Ouannas, A., Oussaeif, T.E., Grassi, G., Batiha, I.M., Momani, S.: On variable-order fractional discrete neural networks: solvability and stability. Fractal and Fract. 6, 119 (2022)

    Article  Google Scholar 

  10. Abbes, A., Ouannas, A., Shawagfeh, N.: Incommensurate fractional discrete neural network: chaos and complexity. Eur. Phys. J. Plus 137, 1–15 (2022)

    Article  Google Scholar 

  11. Ouannas, A., Batiha, I.M., Bekiros, S., Liu, J., Jahanshahi, H., Aly, A.A., Alghtani, A.H.: Synchronization of the glycolysis reaction-diffusion model via linear control law. Entropy 23, 1516 (2021)

    Article  MathSciNet  Google Scholar 

  12. Debbouche, N., Ouannas, A., Batiha, I.M., Grassi, G., Kaabar, M.K.A., Jahanshahi, H., Aly, A.A., Aljuaid, A.M.: Chaotic behavior analysis of a new incommensurate fractional-order Hopfield neural network system. Complexity 2021, 3394666 (2021)

    Article  Google Scholar 

  13. Batiha, I.M., Ouannas, A., Emwas, J.A.: A stabilization approach for a novel chaotic fractional-order discrete neural network. J. Math. Comput. Sci. 11, 5514–5524 (2021)

    Google Scholar 

  14. Mellah, M., Ouannas, A., Khennaoui, A.A.: Fractional discrete neural networks with different dimensions: coexistence of complete synchronization, antiphase synchronization and full state hybrid projective synchronization. Nonlinear Dyn. Syst. Theory 21, 410 (2021)

    MathSciNet  Google Scholar 

  15. Zhou, J., Yang, Y., Zhang, T.: Global dynamics of a reaction-diffusion waterborne pathogen model with general incidence rate. J. Math. Anal. Appl. 466, 835–859 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yang, Y., Zhou, J.: Global stability of a discrete virus dynamics model with diffusion and general infection function. Int. J. Comput. Math. 96, 1752–1762 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  17. Elaydi, S.: An Introduction to Difference Equations. Springer, San Antonio, Texas (2015)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid, 2600, Jordan

    Nidal Anakira

  2. Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria

    Amel Hioual, Adel Ouannas & Taki-Eddine Oussaeif

  3. Department of Mathematics, Al Zaytoonah University of Jordan, Amman, 11733, Jordan

    Iqbal M. Batiha

  4. Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE

    Iqbal M. Batiha

Authors
  1. Nidal Anakira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amel Hioual
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Adel Ouannas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Taki-Eddine Oussaeif
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Iqbal M. Batiha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nidal Anakira .

Editor information

Editors and Affiliations

  1. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan

    Dia Zeidan

  2. Department of Applied Mathematics, Universitat Politècnica de València, Valencia, Spain

    Juan C. Cortés

  3. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Aliaa Burqan

  4. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Ahmad Qazza

  5. MNZ, Leipzig University of Applied Sciences, Leipzig, Germany

    Jochen Merker

  6. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Gharib Gharib

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Anakira, N., Hioual, A., Ouannas, A., Oussaeif, TE., Batiha, I.M. (2023). Global Asymptotic Stability for Discrete-Time SEI Reaction-Diffusion Model. In: Zeidan, D., Cortés, J.C., Burqan, A., Qazza, A., Merker, J., Gharib, G. (eds) Mathematics and Computation. IACMC 2022. Springer Proceedings in Mathematics & Statistics, vol 418. Springer, Singapore. https://doi.org/10.1007/978-981-99-0447-1_30

Download citation

Publish with us

Policies and ethics

Search

Navigation